It is worth noting that, beside being a class of models for hybrid systems, SMNARX are a particular form of conditional probability Mixtures where component responsibilities depend on the assignments in the preceding time instant, referred to as Hidden Markov Experts in the time series analysis field [1]}. Besides, they constitute an extension of the Hidden Markov Models, widely exploited in the speech recognition context, including conditioned output distribution [2]}. If the Markovian conditioning over the mode switching mechanism is removed - hence loosing the strength of SMNARX reported above - the active state is estimated using the normalized emission probabilities. In fact, such simplification leads to conventional Mixture of Experts previously employed for PWARX and timed switching ARX systems identification [3]}.
